Answer:
the maximum safe operating temperature the engineer should recommend for this reaction is 616 °C
Explanation:
Given the data in the question;
First we calculate the Volume of the steel cylinder;
V = πr²h
radius r = Diameter / 2 = 27 cm / 2 = 13.5 cm
height h = 32.4 cm
so we substitute
V = π × ( 13.5 cm )² × 32.4 cm
V = π × 182.25 cm × 32.4 cm
V = 18550.79 cm³
V = 18.551 L
given that; maximum safe pressure P = 3.10 MPa = 30.5946 atm
vessel contains 0.218kg or 218 gram of carbon monoxide gas
molar mass of carbon monoxide gas is 28.010 g/mol
so
moles of carbon monoxide gas n = 218 gram / 28.010 g/mol = 7.7829 mol
we know that;
PV = nRT
solve for T
T = PV / nR
we know that gas constant R = 0.0820574 L•atm•mol⁻¹ K⁻¹
so we substitute
T = ( 30.5946 × 18.551 ) / ( 7.7829 × 0.082 )
T = 567.5604 / 0.6381978
T = 889.317387 K
T = ( 889.317387 - 273.15 ) °C
T = 616.167 ≈ 616 °C { 3 significant digits }
Therefore, the maximum safe operating temperature the engineer should recommend for this reaction is 616 °C
= 0.800 mol Al